Herman Cain on Tuesday vehemently denied all sexual harassment allegations against him and said he had no memory of the first accuser to publicly describe claimed misconduct by the Republican presidential hopeful.

“They simply didn’t happen. They simply did not happen,” Cain insisted of the accusations of inappropriate sexual behavior, and at least one incident of alleged sexual groping, when he was head of the National Restaurant Association from 1996 to 1999.

At a news conference he held to respond to the latest accusation, made Monday by a Chicago woman who once worked at the restaurant group, Cain described her as a “troubled” woman put up to making false allegations by forces trying to derail his presidential bid.